Question asks:

For which of the following functions of f is f(x) = f(1-x) for all values of x?

a) f(x)=1-x

b) f(x) = 1-x2 (x squared)

c) f(x) x2 - (1-x)2 (in both instances the value of 2 represents the number squared)

d) f(x) = x2 (1-x)2 (again 2 means squared here)

e) f(x) = x/1-x

The answer is D. I started to solve using two values for x but that didn't lead me to the right answer. How can I approach this question to solve?

Many thanks

## Seeking help with f(x) question. Thanks!

##### This topic has expert replies

- GMATGuruNY
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Let x=2.For which of the following functions f is f(x) = f(1-x) for all x?

a. f(x)= 1-x

b. f(x)= 1-xÂ²

c. f(x)= xÂ²-(1-x)Â²

d. f(x)= xÂ²(1-x)Â²

e. f(x)= x/(1-x)

Then f(x) = f(2) and f(1-x) = f(1-2) = f(-1).

The question becomes:

**For which of the following functions does f(2) = f(-1)?**

Answer choice A:

f(2) = 1-2 = -1.

f(-1) = 1-(-1) = 2.

Doesn't work.

Answer choice B:

f(2) = 1 - 2Â² = -3.

f(-1) = 1 - (-1)Â² = 0.

Doesn't work.

Answer choice C:

f(2) = 2Â² - (1-2)Â² = 4 - 1 = 3.

f(-1) = (-1)Â² - [1-(-1)]Â² = 1-4 = -3.

Doesn't work.

Answer choice D:

f(2) = 2Â² * (1-2)Â² = 4 * 1 = 4.

f(-1) = (-1)Â² * [1-(-1)]Â² = 1 * 4 = 4.

Success!

Answer choice E:

f(2) = 2/(1-2) = -2.

f(-1) = (-1)/[(1-(-1)] = -1/2.

Doesn't work.

The correct answer is D.

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- hemant_rajput
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Orla M wrote:Question asks:

For which of the following functions of f is f(x) = f(1-x) for all values of x?

a) f(x)=1-x

b) f(x) = 1-x2 (x squared)

c) f(x) x2 - (1-x)2 (in both instances the value of 2 represents the number squared)

d) f(x) = x2 (1-x)2 (again 2 means squared here)

e) f(x) = x/1-x

The answer is D. I started to solve using two values for x but that didn't lead me to the right answer. How can I approach this question to solve?

Many thanks

I've one more approach.

a.

f(x)= 1-x

say y= 1-x, just to make it more clear.

f(y) = 1 -y

substituting value of y

f(1-x) = 1 - (1-x)

f(1-x) = 1 - 1 + x

f(1-x) = x

f(x) not equal to f(x-1)

b.

f(x) = 1-x^2

f(1-x) = 1 - (1-x)^2 => 1 - (1 + x^2 - 2x)=> 2x - x^2

f(x) not equal to f(x-1)

c.

f(x) = x^2 - (1-x)^2

f(1-x) = (1-x)^2 - (1-(1-x))^2 => (1-x)^2 - (1- 1 + x))^2 => (1-x)^2 - (x)^2

f(x) not equal to f(x-1)

d.

f(x) = x^2 * (1-x)^2

f(1-x) = (1-x)^2 * (1-(1-x))^2 => (1-x)^2 * (1-1+x)^2=>(1-x)^2 * x^2

bingo

f(x) = f(1-x)

I'm no expert, just trying to work on my skills. If I've made any mistakes please bear with me.

one function becomes another function, this is meant by the expression. f(x)=not (1-x) but f(1-x). We are looking for the values of all x to satisfy two functions not defined precisely - only their arguments are given (as x and x-1). By supplying x and x-1 into the functions below we should get the same answers and select the right choice. However, since we don't want to be bogged into calculations we simply set x=0 (x can be any value)

a) f(x)=1-x ==> f(1-x)=1-(1-x)=-x but not 1-x Wrong (even without supplying x=0 here)

b) f(x) = 1-x^2 ==> f(1-x)=1-(1-x)^2=1-(1-2x+x^2)=2x-x^2 but not 1-x^2 Wrong

c) f(x) = x^2-(1-x)^2 ==> f(1-x)=(1-x)^2-(1-(1-x))^2= 1-2x+x^2-(1-(1-2x+x^2)= -4x+2x^2 but not x^2-(1-x)^2 Wrong

d) f(x) = (x^2)*(1-x)^2 ==> f(1-x)=(1-x)^2 *(1-(1-x))^2

we supply x=0 here to make it faster, f(0)=0^2*(1-0)^2=0 and f(0-1)=(0-1)^2 *(1-(1-0))^2=0 good choice

e) f(x) = x/1-x

here too supply x=0 and get f(0)=0 and f(0-1)=(0-1)/(1-(0-1))=-1/2 but not 0 Wrong

answer d

a) f(x)=1-x ==> f(1-x)=1-(1-x)=-x but not 1-x Wrong (even without supplying x=0 here)

b) f(x) = 1-x^2 ==> f(1-x)=1-(1-x)^2=1-(1-2x+x^2)=2x-x^2 but not 1-x^2 Wrong

c) f(x) = x^2-(1-x)^2 ==> f(1-x)=(1-x)^2-(1-(1-x))^2= 1-2x+x^2-(1-(1-2x+x^2)= -4x+2x^2 but not x^2-(1-x)^2 Wrong

d) f(x) = (x^2)*(1-x)^2 ==> f(1-x)=(1-x)^2 *(1-(1-x))^2

we supply x=0 here to make it faster, f(0)=0^2*(1-0)^2=0 and f(0-1)=(0-1)^2 *(1-(1-0))^2=0 good choice

e) f(x) = x/1-x

here too supply x=0 and get f(0)=0 and f(0-1)=(0-1)/(1-(0-1))=-1/2 but not 0 Wrong

answer d

Orla M wrote:Question asks:

For which of the following functions of f is f(x) = f(1-x) for all values of x?

a) f(x)=1-x

b) f(x) = 1-x2 (x squared)

c) f(x) x2 - (1-x)2 (in both instances the value of 2 represents the number squared)

d) f(x) = x2 (1-x)2 (again 2 means squared here)

e) f(x) = x/1-x

The answer is D. I started to solve using two values for x but that didn't lead me to the right answer. How can I approach this question to solve?

Many thanks

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